I was playing through Abe Lincoln Must Die! when a bug happened to me- as I threw the beacon onto the galloping Lincoln, the game briefly took control out of my hands and ran a couple lines of dialogue between Sam & Max ("Better hope he doesn't gnaw his back off trying to remove that beacon!" or something). Anyway, right near the very end of those dialogue lines, I realized that while I couldn't see my mouse cursor, the buttons on the screen allowing me to quickly go from driving mode to another game area would still highlight, so I moved the phantom cursor over the White House button and clicked, thereby interrupting the dialogue and taking me back to Max's new office. Unfortunately, I assume the trigger that says "Lincoln.Beacon=1" (or whatever) isn't set to activate until after the dialogue is finished, since when I went back to the War Room (the beacon now gone from my inventory), the targeting computer still showed the view of Bosco's shop, the beacon was not on Abe's back, and the actual inconvenience store area was completely devoid of beacons as well. Lucky for me, I had recently saved, since going back and letting those dialogue lines finish was the only way I could complete the game.
The good thing is that (from my very limited knowledge of game design), this should be an easy fix for you guys- just setting the trigger to activate as soon as the dialogue lines start- but as of now, it's an issue that needs to be addressed.